Method for determining optimal abs slip and deceleration thresholds

ABSTRACT

A vehicle anti-lock braking system includes a brake pedal and a brake modulator. The brake system reduces braking pressure by an initial pressure reduction after detecting insipient wheel lock. Vehicle deceleration is measured as a function of brake pedal position. A first table is updated with the vehicle deceleration and the brake pedal position. A coefficient of friction of a road surface is estimated based on the first table. Wheel slip and deceleration target thresholds are determined based on the coefficient of friction. The wheel slip and deceleration target thresholds are used to populate a command table for the anti-lock braking system. Brake heat, brake torque, vehicle weight and grade are estimated. Release and apply pressures are calculated from an adjusted coefficient of friction, a coefficient of friction and the grade.

TECHNICAL FIELD

[0001] The present invention relates to vehicle anti-lock brakingsystems, and more particularly to a system and method for determininganti-lock braking slip and deceleration thresholds.

BACKGROUND OF THE INVENTION

[0002] Motor vehicle anti-lock braking systems modulate hydraulic brakepressures upon detection of insipient wheel lock to maximize frictionbetween tires of a vehicle and a road surface. At incipient wheel lock,the brake pressures are initially reduced by an amount that is based onan assumed coefficient of friction between the tires of the vehicle andthe road surface. The brake pressures are re-applied once theacceleration of the wheels exceed a predetermined acceleration value.

[0003] Since the coefficient of friction is ordinarily unknown, theinitial brake pressure reduction is typically calculated for aworst-case road surface, such as glare ice. This approach provides asomewhat degraded braking performance when the road surface has arelatively high coefficient of friction. Most road surfaces havesubstantially higher coefficients of friction than glare ice. In otherwords, the brake pressures are reduced more than is typically requiredby the road surface.

[0004] After the initial brake pressure reduction, the coefficient offriction is estimated based on a time period that is required for thewheels to accelerate to the reference acceleration value. The rate ofbrake pressure re-application is determined based on the estimatedcoefficient of friction. Although the coefficient of friction can beinitially estimated from the brake pressure or the brake pedal force,the sensors for obtaining such information significantly increase thecost of the anti-lock braking system. The estimated coefficient offriction is subject to errors when the relationship between brakepressure and brake torque deviates from the norm.

[0005] Some conventional anti-lock braking systems include a “peakseeking” control method that slowly adjusts the wheel slip and wheeldeceleration thresholds by applying rate controlled brake pressureincreases. This peak seeking method may require several apply andrelease cycles to find the correct slip and deceleration targetthresholds. Time wasted during the peak seeking control method lengthensthe total stopping distance on all surface types.

SUMMARY OF THE INVENTION

[0006] A control system and method according to the present inventionoperates a vehicle anti-lock braking system. The braking system includesa brake pedal and a brake modulator. The brake system reduces brakingpressure by an initial pressure reduction after detecting insipientwheel lock. Vehicle deceleration is measured as a function of brakepedal position. A first table is updated with the vehicle decelerationand the brake pedal position. A coefficient of friction of a roadsurface is estimated based on the first table. Wheel slip anddeceleration target thresholds are determined based on the coefficientof friction.

[0007] In other features, the wheel slip and deceleration targetthresholds are used to populate a command table for the anti-lockbraking system. Brake heat, brake torque, vehicle weight and grade areestimated.

[0008] In still other features, a wheel recovery timer is set equal tozero. Onset vehicle speed is determined. An actual recovery time that isrequired for wheels of the vehicle to accelerate to a predeterminedacceleration level is timed. An expected recovery time is calculated andcompared to the actual recovery time.

[0009] In yet other features, a recovery delta is calculated based onthe expected and actual recovery times. The coefficient of friction isupdated if the recovery delta is greater than a first constant. Anadjusted coefficient of friction is calculated based on the recoverydelta and the coefficient of friction. Wheel slip is calculated based onthe adjusted coefficient of friction, the coefficient of friction, andthe target wheel slip. Wheel deceleration is calculated based on theadjusted coefficient of friction, the coefficient of friction, and thetarget wheel deceleration. The command table is updated with the wheelslip and deceleration. Release and apply pressures are calculated fromthe adjusted coefficient of friction, the coefficient of friction andthe grade.

[0010] Further areas of applicability of the present invention willbecome apparent from the detailed description provided hereinafter. Itshould be understood that the detailed description and specificexamples, while indicating the preferred embodiment of the invention,are intended for purposes of illustration only and are not intended tolimit the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

[0012]FIG. 1 is a functional block diagram of an anti-lock brakingsystem according to the present invention;

[0013]FIG. 2 is a graph showing deceleration as a function of brakepedal position;

[0014]FIG. 3 is a graph showing deceleration as a function of threebrake pedal positions;

[0015]FIG. 4 is a table showing deceleration as a function of slip; and

[0016]FIG. 5 is a flowchart illustrating exemplary steps performed bythe anti-lock braking system according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0017] The following description of the preferred embodiment(s) ismerely exemplary in nature and is in no way intended to limit theinvention, its application, or uses.

[0018] Referring to FIG. 1, an anti-lock braking system (ABS) 10 isshown. A vehicle 12 includes hydraulically activated friction brakes 14,16, 18, and 20 at vehicle wheels 22, 24, 26, and 28, respectively. Adriver-actuated brake pedal 30 is mechanically and/or electricallycoupled to a master cylinder (MC) 32 for producing hydraulic pressure inproportion to the force that is applied to the brake pedal 30.

[0019] The master cylinder 32, which may include a pneumatic booster(not shown), proportions the hydraulic pressure between front and rearbrake supply lines 34 and 36 in a conventional manner. The front supplyline 34 is coupled to the left front (LF) brake 14 by a LF anti-lockmodulator (M) 38 and to the right front (RF) brake 16 by a RF anti-lockmodulator (M) 40. The rear supply line 36 is coupled to the left andright rear wheel brakes 18 and 20 by a rear anti-lock modulator (M) 42.

[0020] An ABS controller 50 receives various inputs, including wheelspeed signals on lines 52, 54, 56, and 58 from wheel speed sensors 60,62, 64, and 66, respectively. The ABS controller 50 receives a brakepedal position signal PP on line 68 from pedal position sensor 70. Inresponse to the various inputs, the ABS controller 50 outputs modulatorcontrol signals on lines 72, 74, and 76 during wheel lock-up conditions.The ABS controller 50 may also output diagnostic information signals fordisplay on a driver information device (not shown) associated with aninstrument panel. The ABS controller 50 preferably includes a processor,an input/output (I/O) interface, and memory such as read-only memory(ROM), random access memory (RAM), flash memory and/or other suitableelectronic storage. The ABS controller 50 can also be implemented as anapplication specific integrated circuit (ASIC).

[0021] In general, the ABS controller 50 monitors the measured wheelspeeds to detect a condition of insipient wheel lock. The controller 50adjusts modulators 38, 40, and 42 to modulate the respective hydraulicbrake pressures to maximize the tractive force between the vehicle tiresand the road surface. When insipient wheel lock is detected, themodulators 38, 40, and 42 are activated to rapidly reduce the respectivebrake pressures to eliminate wheel slip. The amount of pressurereduction that is required to eliminate wheel slip varies with thecoefficient of friction between the tires and the road surface.Conventional ABS assume a low coefficient of friction such as glare icesince the actual coefficient of friction of the road surface isordinarily unknown.

[0022] The reduction in brake pressure allows the wheels 22, 24, 26, and28 to accelerate. The control unit 50 measures the time that is requiredfor the wheel acceleration to reach a reference acceleration value.Conventional ABS estimate the coefficient of friction based on themeasured time. The modulators 38, 40, and 42 are controlled to re-applybrake pressures based on the estimated coefficient(s) of friction.

[0023] The ABS according to the present invention estimates thecoefficient of friction between the tires and the road surface prior tothe initial pressure reduction. For example, if the coefficient offriction is relatively high, the initial pressure reduction can berelatively small and the performance of the ABS is improved. Brakepressure can be rapidly re-applied once the wheel acceleration reachesthe reference acceleration value. As a result, shorter stoppingdistances are produced.

[0024] In “Anti-Lock Brake Control Method Having Adaptive Initial BrakePressure Reduction”, U.S. Ser. No. 09/882,795, filed Jun. 18, 2001,which is hereby incorporated by reference, the ABS adaptively determinesthe coefficient of friction of the road surface. The ABS describedtherein determines the initial brake pressure reduction when insipientwheel lock occurs. The coefficient of friction is computed based onbrake torque and vehicle weight. Brake torque and vehicle weight areadaptively determined based on a periodically updated table defining arelationship between brake pedal position and vehicle deceleration. Therelationship is corrected for variations in brake heating.

[0025]FIG. 2 graphically depicts a representative relationship betweenvehicle deceleration and brake pedal position for braking of the vehicle12. The relationship assumes that there is no lock-up condition and themodulators 38, 40, and 42 are inactive. Typically, a lower “knee”portion of the relationship varies considerably from stop to stop. Theportion of the relationship above the knee portion tends to be linearand repeatable from stop to stop. For this reason, the lower kneeportion of the relationship is preferably not used. The brake pedalposition vs. vehicle deceleration relationship is preferablycharacterized for pedal positions and vehicle decelerations in thelinear portion above the knee portion.

[0026] Braking characterization data is collected by determining pedalpositions that correspond to a plurality of different vehicledeceleration values. For example, in FIG. 3, deceleration values D1, D2and D3 correspond to pedal position values Pvsd(0), Pvsd(1), andPvsd(2). The braking data is collected during braking operation when thepedal 30 is depressed at a “normal” rate or held in a static positionfor a predetermined period. Data is not collected while the brake pedal30 is released or during panic braking. This eliminates the need tocompensate for dynamic effects such as suspension, powertrain, tire andsensor dynamics.

[0027] The vehicle acceleration at the onset of braking is saved andsubtracted from the deceleration during the braking operation tocompensate for the effects of engine braking and the grade of the road.The road grade and other factors such as vehicle weight and brakeheating may be estimated and used to compensate the collected brakingdata. For example, in U.S. Pat. No. 6,212,458 to Walenty et al., issuedon Apr. 3, 2001, which is hereby incorporated by reference, the ABSestimates grade, vehicle weight and brake heating.

[0028] The ABS according to the present invention identifies correctslip and deceleration thresholds based on the initial brake pressurereduction that is described above and a current brake efficiency. Thisapproach for identifying ABS slip and deceleration target thresholdsinvolves estimating a current state of health of the brake system andgenerating a current pedal position versus brake output torque.

[0029] The present invention uses surface mu to calculate brake heat,vehicle weight, and grade. Surface mu is calculated using a currentpedal position versus deceleration table. The following equations aredescribed in further detail in “Anti-Lock Brake Control Method HavingAdaptive Initial Brake Pressure Reduction”, U.S. Ser. No. 09/882,795,filed Jun. 18, 2001: $\begin{matrix}\begin{matrix}{{Brake\_ Heat} = {{Brake\_ Heat} - \left( {\left( {{MPH} + {Kcoolspdmin}} \right)^{2}*} \right.}} \\{\left. {Kcoolspd} \right)*\left( {{Brake\_ Heat} - \left( {{Brake\_ Heat}*} \right.} \right.} \\{\left. {Kcoolambient} \right) + \left( {{Brake}\quad {Torque}*} \right.} \\{\left. \left( {{Kheat}*{MPH}} \right) \right)*{\left( {{Kmaxtemp} - {Brake\_ Heat}} \right)/}} \\\left. {Kmaxtemp} \right)\end{matrix} & (1) \\\begin{matrix}{{Brake\_ Torque} = \left( \left( {{{Pedal}\quad {Position}} - {\left( {{Pvsd}(0)} \right)*}}\quad \right. \right.} \\{{\left. {~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\left( {\left( {{{Pvsd}(2)} - {{Pvsd}(0)}} \right)/\left( {{D3} - {D1}} \right)} \right) \right)*}\quad} \\{\left. \quad {Kbrk\_ torque} \right) + \left( \left( {{{Update\_ Brake}{\_ heat}} -}\quad \right. \right.} \\{\left. {\left. {~~~}{Brake\_ heat} \right)*{Kheat\_ crv}} \right)\quad}\end{matrix} & (2) \\\begin{matrix}{{Vehicle\_ Weight} = {{LVW} + \left( \left( \left( \left( {{{Pvsdold}(2)} - \left( {{Pvsdold}(0)} \right) -} \right. \right. \right. \right.}} \\{\left. \left( {\left( {{{Pvsd}(2)} - {{Pvsd}(0)}} \right)/\left( {{D3} - {D1}} \right)} \right) \right)*} \\{\left. {Kveh\_ weight} \right) + \left( \left( {{{Update\_ Brake}{\_ heat}} -} \right. \right.} \\\left. {\left. {Brake\_ heat} \right)*{Kheat\_ crv}} \right)\end{matrix} & (3) \\\begin{matrix}{{Grade} = {{{Rolling}\quad {Resistance}} + {{Aerodynamic}\quad {Drag}} +}} \\{{~~~~~~~~~~~~~~~~~~~}{{{Engine}\quad {Braking}} + {{Brake}\quad {Torque}} + {Accel}}}\end{matrix} & (4) \\\begin{matrix}{{Surface\_ Mu} = {\left( {{Brake\_ Torque}/{Vehicle\_ Weight}} \right)*}} \\{{Kmu\_ Lambda}}\end{matrix} & (5)\end{matrix}$

[0030] where variables starting with a K are stored and/or calculatedvalues.

[0031] Upon initial surface-based brake pressure reduction, wheel slipand decel target thresholds are initially set to reflect an initialcoefficient of friction of the road surface. Where:

[0032] (6) Slip_TargetLF & RF=Kmax_slip_Front*Surface_Mu

[0033] (7) Slip_TargetLR & RR=Kmax_slip_Rear*Surface_Mu

[0034] (8) DecelLF_& RF=Kmaxdecel_Front*Surface_Mu

[0035] (9) DecelLR_& RR=Kmax_decel_Rear*Surface_Mu

[0036] The slip and deceleration are used to fill positions in four ABScommand look-up tables of the controller 50 where: $\begin{matrix}\begin{matrix}{{{ABS\_ TableLF}\left( {i,j} \right)} = {\left( {{Kslip\_ front}\left( {i,j} \right)*{Slip\_ TargetLF}} \right) +}} \\{\left( {{Kdecel\_ front}\left( {i,j} \right)*{Decel\_ TargetLF}} \right)}\end{matrix} & (10) \\\begin{matrix}{{{ABS\_ TableLR}\left( {i,j} \right)} = {\left( {{Kslip\_ C}\left( {i,j} \right)*{Slip\_ TargetLR}} \right) +}} \\{\left( {{Kdecel\_ Rear}\left( {i,j} \right)*{Decel\_ TargetLR}} \right)}\end{matrix} & (11) \\\begin{matrix}{{{ABS\_ TableRF}\left( {i,j} \right)} = {\left( {{Kslip\_ front}\left( {i,j} \right)*{Slip\_ TargetRF}} \right) +}} \\{\left( {{Kdecel\_ front}\left( {i,j} \right)*{Decel\_ TargetRF}} \right)}\end{matrix} & (12) \\\begin{matrix}{{{ABS\_ TableRR}\left( {i,j} \right)} = {\left( {{Kslip\_ C}\left( {i,j} \right)*{Slip\_ TargetRR}} \right) +}} \\{\left( {{Kdecel\_ Rear}\left( {i,j} \right)*{Decel\_ TargetRR}} \right)}\end{matrix} & (13)\end{matrix}$

[0037] Referring now to FIG. 4, an ABS Table is shown. Before theinitial pressure release, a wheel recovery timer, for exampleRecovery_LFc, is set to zero. The onset vehicle speed, Ovspd, is saved.Each timer is incremented for every real-time control loop until eachwheel has re-accelerated to a predetermined level. The amount of timerequired for each wheel to recover is used to calculate the slip anddecel targets. Where:

[0038] (14) Expected Recovery_Time=(Surface_mu*Ovspd)*Krecovery_Time

[0039] (15) Recovery_Delta=Expected_Recovery_Time/Recovery_LFc

[0040] The following is a high to low coefficient surface change test.If true, the surface mu must be changed to reflect this occurrence. Inother words, the original surface mu is no longer valid.

[0041] (16) If Recovery_Delta>Khi_to_lo_co (0.2) then

[0042] (17) Surface_mu=Recovery_Delta*KT_mu

[0043] A surface mu adjustment is calculated using the recovery timedelta and the original surface mu. This adjustment along with theoriginal surface mu forms the new slip and decel targets:$\begin{matrix}{{{Surface\_ mu}{\_ adj}} = {{Recovery\_ Delta}*{Surface\_ mu}}} & (18) \\\begin{matrix}{{Slip\_ TargetLF} = {{Slip\_ TargetLF} + {{Kmax\_ slip}{\_ Front}*}}} \\{\left( {{Surface\_ mu} + {{Surface\_ mu}{\_ adj}}} \right)}\end{matrix} & (19) \\\begin{matrix}{{Decel\_ TargetRR} = {{Decel\_ TargetRR} + {{Kmax\_ decel}{\_ Rear}*}}} \\{\left( {{Surface\_ Mu} + {{Surface\_ mu}{\_ adj}}} \right)}\end{matrix} & (20)\end{matrix}$

[0044] The slip and deceleration terms are used to fill each position inthe four ABS command lookup tables where: $\begin{matrix}\begin{matrix}{{{ABS\_ TableLF}\left( {i,j} \right)} = {\left( {{Kslip\_ front}\left( {i,j} \right)*{Slip\_ TargerLF}} \right) +}} \\{\left( {{Kdecel\_ front}\left( {i,j} \right)*{Decel\_ TargetLF}} \right)}\end{matrix} & (21) \\\begin{matrix}{{{ABS\_ TableLR}\left( {i,j} \right)} = {\left( {{Kslip\_ C}\left( {i,j} \right)*{Slip\_ TargetLR}} \right) +}} \\{\left( {{Kdecel\_ Rear}\left( {i,j} \right)*{Decel\_ TargetLR}} \right)}\end{matrix} & (22)\end{matrix}$

[0045] The release and apply pressures are calculated from the averagesurface mu: $\begin{matrix}\begin{matrix}{{{Front\_ Release}{\_ PSI}} = {{KmaxF\_ PSI}*\left( {1 - \left( {{{Surface\_ Mu}{\_ adj}} +} \right.} \right.}} \\{{\left. {Surface\_ Mu} \right)/2} - \left( {{Grade}*} \right.} \\\left. \left. {Kweight\_ transfer} \right) \right)\end{matrix} & (23) \\\begin{matrix}{{{Rear\_ Release}{\_ PSI}} = {{KmaxR\_ PSI}*\left( {1 - \left( {{{Surface\_ Mu}{\_ adj}} +} \right.} \right.}} \\{{\left. {Surface\_ Mu} \right)/2} - \left( {{Grade}*} \right.} \\\left. \left. {Kweight\_ transfer} \right) \right)\end{matrix} & (24) \\\begin{matrix}{{{Front\_ Apply}{\_ PSI}} = {{KmaxF\_ PSI}*\left( {1 - {{Surface\_ Mu}{\_ adj}} +} \right.}} \\{{\left. {Surface\_ Mu} \right)/2} - \left( {{Grade}*} \right.} \\\left. \left. {Kweight\_ transfer} \right) \right)\end{matrix} & (25) \\\begin{matrix}{{{Rear\_ Apply}{\_ PSI}} = {{KmaxR\_ PSI}*\left( {1 - \left( {{{Surface\_ Mu}{\_ adj}} +} \right.} \right.}} \\{{\left. {Surface\_ Mu} \right)/2} - \left( {{Grade}*} \right.} \\\left. \left. {Kweight\_ transfer} \right) \right)\end{matrix} & (26)\end{matrix}$

[0046] Referring now to FIG. 5, a method executed by the ABS controller50 is shown. Control starts in step 100. In step 102, the ABS controller50 reads brake pedal position, vehicle speeds, form slip, and formdecel. The controller 50 records pedal pos vs. decel table. The ABScontroller 50 calculates brake heat, brake torque, vehicle weight,grade, and surface mu. The ABS controller 50 looks up anABS_Table(decel,Slip) command.

[0047] In step 104, the ABS controller 50 determines whether the ABSflag is true. If not, control continues with step 108 where the ABScontroller 50 determines whether the ABS_Table command is equal torelease. If true, control continues with step 110 and a recovery_time isincremented. Control continues with step 114 and an ABS command isexecuted. If step 108 is false, control continues with step 116 wherecontrol sets recovery_delta=expected_recovery_time/recovery_time.

[0048] In step 118, the controller 50 determines whether recovery deltais greater than a constant K_hi_to_lo_co. If true, control continueswith step 120 and sets surface_mu=recovery_delta*KT_mu andsurface_mu_adj=surface_mu. Otherwise, control continues from step 118 tostep 122 where the controller 50 calculates the following:

[0049] (27) Surface_Mu_adj=Recovery_Delta*Surface_Mu;

[0050] (28) A_Mu=(Surface_Mu+Surface_Mu_adj)/2;

[0051] (29) Slip_target_Front=Kmaxslip*A_Mu;

[0052] (30) Slip_target_Rear=Kmaxslip*A_Mu;

[0053] (31) Decel_target_Front=Kmaxslip*A_Mu;

[0054] (32) Decel_target_Rear=Kmaxslip*A_Mu; and

[0055] (33) ABS_Table(i,j)=(Kslip_front(i,j)*Slip_Target(i,j)+(Kdecel_Front(i,j)*Decel_Target).

[0056] Control continues from step 122 to step 124 where the ABScontroller 50 calculates the following: $\begin{matrix}\begin{matrix}{{{Front\_ Release}{\_ PSI}} = {{KRmaxF\_ PSI}*\left( {1 - {A\_ Mu} -} \right.}} \\\left. \left( {{Grade}*{Kwt\_ Transfer}} \right) \right)\end{matrix} & (34) \\\begin{matrix}{{{Rear\_ Release}{\_ PSI}} = {{KRmaxR\_ PSI}*\left( {1 - {A\_ Mu} -} \right.}} \\\left. \left( {{Grade}*{Kwt\_ Transfer}} \right) \right)\end{matrix} & (35) \\\begin{matrix}{{{Front\_ Apply}{\_ PSI}} = {{KAmaxF\_ PSI}*\left( {1 - {{A\_ Mu}\_} -} \right.}} \\\left. \left( {{Grade}*{Kwt\_ Transfer}} \right) \right)\end{matrix} & (36) \\\begin{matrix}{{{Rear\_ Apply}{\_ PSI}} = {{KAmaxR\_ PSI}*\left( {1 - {{A\_ Mu}\_} -} \right.}} \\\left. \left( {{Grade}*{Kwt\_ Transfer}} \right) \right)\end{matrix} & (37) \\{{{Recovery\_ Time} = 0},{{Recovery\_ Delta} = 0},{{Ovspd} = {Vspd}}} & (38) \\\begin{matrix}{{{Expected\_ Recovery}{\_ Time}} = {\left( {{Surface\_ Mu}*{Ovspd}} \right)*}} \\{{Krecovery\_ Time}}\end{matrix} & (38)\end{matrix}$

[0057] Control continues from step 124 to step 114 where the ABScontroller 50 executes an ABS command.

[0058] If the ABS flag is not equal to true, control continues from step104 to step 130 where the ABS controller 50 determines whether incipientwheel lock is present. If not, control continues with step 114.Otherwise, control continues with step 134 where the ABS controller 50calculates the following:

[0059] (40) ABS=True;

[0060] (41) Ovspd=Vspd; $\begin{matrix}\begin{matrix}{{{Brake}\quad {Torque}\quad {Release}} = {{Kmax\_ release}{\_ psi}*\left( {1 -} \right.}} \\{{{Surface\_ Mu} - \left( {{Grade}*} \right.}} \\{\left. \left. {Kweight\_ transfer} \right) \right);}\end{matrix} & (42) \\{{{{Slip\_ target}{\_ Front}} = {{Kmaxslip}*{Surface\_ Mu}}};} & (43) \\{{{{Decel\_ target}{\_ Front}} = {{Kmaxslip}*{Surface\_ Mu}}};} & (44) \\{{{{Slip\_ target}{\_ Rear}} = {{Kmaxslip}*{Surface\_ Mu}}};} & (45) \\{{{{Decel\_ target}{\_ Rear}} = {{Kmaxslip}*{Surface\_ Mu}}};} & (46) \\\begin{matrix}{{{Fill}\quad {ABS\_ TableF}\left( {i,j} \right)} = {\left( {{Kslip\_ front}*{Slip\_ Target}} \right) +}} \\{{{Kdecel\_ front}*}} \\{\left. {Decel\_ Target} \right);{and}}\end{matrix} & (47) \\\begin{matrix}{{{Fill}\quad {ABS\_ TableR}\left( {i,j} \right)} = {\left( {{Kslip\_ rear}*{Slip\_ Target}} \right) +}} \\{{{Kdecel\_ rear}*}} \\{\left. {Decel\_ Target} \right).}\end{matrix} & (48)\end{matrix}$

[0061] Control continues from step 134 to step 136 where the ABScontroller 50 releases pressure and setsexpected_recovery_time=(Surface_Mu*Ovspd)*Krecovery_Time. Controlcontinues from step 136 to step 114.

[0062] Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the present invention can beimplemented in a variety of forms. Therefore, while this invention hasbeen described in connection with particular examples thereof, the truescope of the invention should not be so limited since othermodifications will become apparent to the skilled practitioner upon astudy of the drawings, the specification and the following claims.

1. A method of operating a vehicle anti-lock braking system including a brake pedal and a brake modulator that reduces braking pressure by a initial pressure reduction after detecting insipient wheel lock, comprising: measuring vehicle deceleration as a function of brake pedal position; updating a first table with said vehicle deceleration and said brake pedal position; estimating a coefficient of friction of a road surface based on said first table; and determining wheel slip and deceleration target thresholds based on said coefficient of friction.
 2. The method of claim 1 further comprising using said wheel slip and deceleration target thresholds to populate a command table for said anti-lock braking system.
 3. The method of claim 2 further comprising estimating brake heat.
 4. The method of claim 3 wherein said brake heat is estimated using the following equation: Brake_Heat−((MPH+Kcoolspdmin)² *Kcoolspd)*(Brake_Heat−(Brake_Heat*Kcoolambient)+(Brake Torque*(Kheat*MPH))*(Kmaxtemp−Brake_Heat)/Kmaxtemp).
 5. The method of claim 3 further comprising estimating brake torque.
 6. The method of claim 5 wherein said brake torque is calculated using the following equation: ((Pedal Position−(Pvsd(0))*((Pvsd(2)−Pvsd(0))/(D3−D1)))*Kbrk _(—) torque)+(Update_Brake_heat−Brake_heat)*Kheat _(—) crv)
 7. The method of claim 5 further comprising estimating vehicle weight.
 8. The method of claim 7 wherein said vehicle weight is estimated using the following equation: LVW+((((Pvsdold(2)−(Pvsdold(0))−((Pvsd(2)−Pvsd(0))/(D3−D1)))*Kveh _(—) weight)+((Update_Brake_heat−Brake_heat)*Kheat _(—) crv)
 9. The method of claim 7 wherein said coefficient of friction is calculated using the following equation (Brake_Torque/Vehicle_Weight)*Kmu_Lambda.
 10. The method of claim 7 further comprising calculating grade.
 11. The method of claim 10 wherein said grade is calculated using the following equation: Rolling Resistance+Aerodynamic Drag+Engine Braking+Brake Torque+Accel.
 12. The method of claim 10 further comprising: setting a wheel recovery timer equal to zero; determining onset vehicle speed; measuring an actual recovery time by timing acceleration of wheels of said vehicle to a predetermined acceleration level; calculating an expected recovery time; and calculating a recovery delta based on said expected and actual recovery times.
 13. The method of claim 12 further comprising: updating said coefficient of friction if said recovery delta is greater than a first constant.
 14. The method of claim 13 further comprising calculating an adjusted coefficient of friction based on said recovery delta and said coefficient of friction.
 15. The method of claim 14 further comprising calculating wheel slip based on said adjusted coefficient of friction, said coefficient of friction, and said target wheel slip.
 16. The method of claim 14 further comprising calculating wheel deceleration based on said adjusted coefficient of friction, said coefficient of friction, and said target wheel deceleration.
 17. The method of claim 16 further comprising updating said command table with said wheel slip and deceleration.
 18. The method of claim 17 further comprising calculating release and apply pressures from said adjusted coefficient of friction, said coefficient of friction and said grade.
 19. A vehicle anti-lock braking system comprising: a brake pedal; a brake modulator; and a controller that communicates with said brake modulator and that measures vehicle deceleration as a function of brake pedal position, updates a first table with said vehicle deceleration and said brake pedal position, estimates a coefficient of friction of a road surface based on said first table, and determines wheel slip and deceleration target thresholds based on said coefficient of friction.
 20. The vehicle anti-lock braking system of claim 19 wherein said controller uses said wheel slip and deceleration target thresholds to populate a command table for said anti-lock braking system.
 21. The vehicle anti-lock braking system of claim 20 wherein said controller estimates brake heat.
 22. The vehicle anti-lock braking system of claim 21 wherein said brake heat is estimated using the following equation: Brake_Heat−((MPH+Kcoolspdmin)² *Kcoolspd)*(Brake_Heat−(Brake_Heat*Kcoolambient)+(Brake Torque*(Kheat*MPH))*(Kmaxtemp−Brake_Heat)/Kmaxtemp).
 23. The vehicle anti-lock braking system of claim 21 wherein said controller estimates brake torque.
 24. The vehicle anti-lock braking system of claim 23 wherein said brake torque is calculated using the following equation: ((Pedal Position−(Pvsd(0))*((Pvsd(2)−Pvsd(0))/(D3−D1)))*Kbrk _(—) torque)+(Update_Brake_heat−Brake_heat)*Kheat _(—) crv)
 25. The vehicle anti-lock braking system of claim 23 wherein said controller estimates vehicle weight.
 26. The vehicle anti-lock braking system of claim 25 wherein said vehicle weight is estimated using the following equation: LVW+((((Pvsdold(2)−(Pvsdold(0))−((Pvsd(2)−Pvsd(0))/(D3−D1)))*Kveh _(—) weight)+((Update_Brake_heat−Brake_heat)*Kheat _(—) crv)
 27. The vehicle anti-lock braking system of claim 25 wherein said coefficient of friction is calculated using the following equation: (Brake_Torque/Vehicle_Weight)*Kmu_Lambda.
 28. The vehicle anti-lock braking system of claim 25 wherein said controller estimates grade.
 29. The vehicle anti-lock braking system of claim 25 wherein said grade is calculated using the following equation: Rolling Resistance+Aerodynamic Drag+Engine Braking+Brake Torque+Accel.
 30. The vehicle anti-lock braking system of claim 28 further comprising: setting a wheel recovery timer equal to zero; determining onset vehicle speed; measuring an actual recovery time by timing acceleration of wheels of said vehicle to a predetermined acceleration level; calculating an expected recovery time; and calculating a recovery delta based on said expected and actual recovery times.
 31. The vehicle anti-lock braking system of claim 30 wherein said controller updates said coefficient of friction if said recovery delta is greater than a first constant.
 32. The vehicle anti-lock braking system of claim 31 wherein said controller calculates an adjusted coefficient of friction based on said recovery delta and said coefficient of friction.
 33. The vehicle anti-lock braking system of claim 32 wherein said controller calculates wheel slip based on said adjusted coefficient of friction, said coefficient of friction, and said target wheel slip.
 34. The vehicle anti-lock braking system of claim 33 wherein said controller calculates wheel deceleration based on said adjusted coefficient of friction, said coefficient of friction, and said target wheel deceleration.
 35. The vehicle anti-lock braking system of claim 34 wherein said controller updates said command table with said wheel slip and deceleration.
 36. The vehicle anti-lock braking system of claim 35 wherein said controller calculates release and apply pressures from said adjusted coefficient of friction, said coefficient of friction and said grade. 